摘要
随着微纳尺度加工技术的飞速发展,MEMS和NEMS器件中的流动与传热问题备受关注。在微纳通道中,气体流动表现出明显的稀薄效应和壁面效应,影响气体与壁面的动量与能量交换。协调系数可以定量描述气固界面的输运现象,其数值越接近于1,气体与壁面的动量与能量交换越充分。本文利用分子动力学(MD)方法研究了切向动量、法向动量以及能量协调系数(TMAC、NMAC、EAC)随温度、壁面构型、表面粗糙度等因素的变化以及气体与壁面的动量和能量交换规律。
论文利用MD方法中截断半径的概念,确定了入射分子与反射分子的状态,进而依据协调系数的定义,提出了MD方法中协调系数的统计算法。
计算结果表明,壁面反射气体分子的法向动量变化是影响气体分子在壁面附近吸附时间长短以及俘获-逃逸行为的主要因素。在光滑通道中,较低的壁面温度和较强的气固相互作用势能使得气体分子的吸附时间较长,TMAC、NMAC和EAC都趋近于1;随着Kn的增大,气体流动的稀薄性增强,气体分子之间的影响逐渐减弱,气体分子的吸附时间减小,TMAC与EAC略有减小。
光滑通道中的壁面具有原子尺度的粗糙度,不同的晶面构型可导致壁面附近的气固作用势能分布不同,较大的法向势能梯度使得气体与壁面的切向动量交换较为充分,TMAC较大,而较大的切向势能梯度则强化了能量交换,导致EAC增大;具有纳米尺度粗糙元的壁面能够很大程度改变壁面附近的气固势能分布,增大法向与切向势能梯度,减小反射分子的平均法向动量。随着粗糙元高度的增加,TMAC和EAC皆逐渐增大,而NMAC逐渐减小。
考虑到三维MD的计算量太大,本文也采用二维MD方法模拟了协调系数。由于在EAC的定义以及壁面构造等方面与三维MD不同,二维MD计算得到的TMAC和EAC比三维结果小,通过二维与三维MD计算结果的对比分析,整理出了关联式,从而可以使用二维结果较好预测三维问题的协调系数。
论文还采用DSMC和MD方法模拟了0.01 < Kn < 0.3的等温流动,将DSMC中的速度分布与滑移理论解对比修正了线性与非线性滑移模型中的滑移系数,利用MD计算得到的TMAC和速度分布修正了一阶滑移系数的表达式。
With the rapid developments of micro- and nanoscale technology, fluid flow and heat transfer in micro/nano electro mechanical systems have drawn more attention. For gas flows in microchannels and nanochannels, the rarefaction and wall effects are evident to induce insufficient momentum and energy exchange between the gas and wall. Accommodation coefficients characterize the transport in gas-solid interfaces quantitatively that the values closer to unity represent more complete momentum and energy exchange. In the present dissertation, the tangential momentum, normal momentum and energy accommodation coefficients (TMAC, NMAC and EAC) are studied using molecular dynamics (MD) method to investigate the effects of temperature, wall lattice configuration and wall roughness on accommodation coefficients as well as gas-wall interactions.
According to the definitions of accommodation coefficients, the statistical algorithm is set up based on the incident and reflected gas molecules determined by cutoff radius in MD method.
The simulation results show that the normal momentum of reflected gas molecules is the key factor affecting the adsorption time and molecular trapping-desorption behaviors near the wall. In smooth channels, lower wall temperature and stronger gas-solid interaction extend the adsorption time so that the TMAC, NMAC and EAC approach unity; with larger Knudsen numbers (Kn) in gas flows, the gas-gas interactions are weakened by strengthen rarefaction so that the TMAC and EAC decrease with less adsorption time.
The lattice configurations of smooth surfaces will induce atomic roughness, and different lattice configurations result in different gas-solid potential energy distributions near the wall. Larger gradient of normal potential leads to larger TMAC and better accommodation of tangential momentum in gas-wall interactions, while larger gradient of tangential potential enhances energy exchange in gas-solid interface and results in a larger EAC. Furthermore, the nanoscale rough cells on the walls alter the distribution of gas-solid potential significantly, in which the gradients of normal and tangential potentials increase and the average normal momentum of reflected molecules decreases bringing longer adsorption time. When the height of rough cells increases, both of the TMAC and EAC increase while the NMAC decreases.
Due to the huge computational costs of three-dimensional (3D) MD method, the accommodation coefficients are also calculated by two-dimensional (2D) MD method in this dissertation. The TMAC and EAC in 2D simulations are smaller than the 3D results since the different EAC expression and wall structures in 3D method. Based on the comparison and analysis of 2D and 3D results, the relations between 2D MD and 3D MD accomodation coefficients are presented. From the relations, the 3D accommodation coefficients can be predicted using 2D ones.
The direct simulation Monte Carlo (DSMC) and MD methods are both employed in the simulations of isothermal flows in the Kn range of 0.01 to 0.3. The first- and second-order slip coefficients in linear and nonlinear slip models are modified by comparing velocity profiles from the DSMC results and the theoretical solutions. With the TMAC and velocity profiles calculated in MD simulations, the modified expression of first-order slip coefficient is presented.
引文
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